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The lift coefficient (CL, CN or Cz) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area. A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. CL is a function of the angle of the body to the flow, its Reynold number and its Mach number. The lift coefficient cl refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.
Contents
Definitions
The lift coefficient CL is defined by
where
resulting in a coeffient:
, for thick airfoils and in marine dynamics the other axis sometimes one choose as the second axis the thickness direction:
resulting in a different coeffient:
The ratio between these two coeffients is the thickness ratio:
The lift coefficient can be approximated using the lifting-line theory, numerically calculated or measured in a wind tunnel test of a complete aircraft configuration.
Section lift coefficient
Lift coefficient may also be used as a characteristic of a particular shape (or cross-section) of an airfoil. In this application it is called the section lift coefficient
The section lift coefficient is based on two-dimensional flow over a wing of infinite span and non-varying cross-section so the lift is independent of spanwise effects and is defined in terms of
where L is the reference length that should always be specified: in aerodynamics and airfoil theory usually the airfoil chord
For a given angle of attack, cl can be calculated approximately using the thin airfoil theory, calculated numerically or determined from wind tunnel tests on a finite-length test piece, with end-plates designed to ameliorate the three-dimensional effects. Plots of cl versus angle of attack show the same general shape for all airfoils, but the particular numbers will vary. They show an almost linear increase in lift coefficient with increasing angle of attack with a gradient known as the lift slope. For a thin airfoil of any shape the lift slope is π2/90 ≃ 0.11 per degree. At higher angles a maximum point is reached, after which the lift coefficient reduces. The angle at which maximum lift coefficient occurs is the stall angle of the airfoil, which is approximately 10 to 15 degrees on a typical airfoil.
Symmetric airfoils necessarily have plots of cl versus angle of attack symmetric about the cl axis, but for any airfoil with positive camber, i.e. asymmetrical, convex from above, there is still a small but positive lift coefficient with angles of attack less than zero. That is, the angle at which cl = 0 is negative. On such airfoils at zero angle of attack the pressures on the upper surface are lower than on the lower surface.